Thermal Corrections to Renyi Entropies for Conformal Field Theories

TL;DR

This paper calculates thermal corrections to Re9nyi entropies in conformal field theories on spheres, using conformal mappings and explicit computations for free scalars, and derives the leading correction to entanglement entropy.

Contribution

It provides a general method to compute thermal corrections to Re9nyi entropies in conformal field theories, including explicit results for free scalars, connecting correlation functions with entropy corrections.

Findings

Derived a formula relating thermal corrections to two-point functions on conical spaces.

Explicitly computed the two-point function for a free conformally coupled scalar.

Reproduced known results for the thermal correction to entanglement entropy.

Abstract

We compute thermal corrections to R\'enyi entropies of $d$ dimensional conformal field theories on spheres. Consider the $n$th R\'enyi entropy for a cap of opening angle $2 \theta$ on $S^{d-1}$. From a Boltzmann sum decomposition and the operator-state correspondence, the leading correction is related to a certain two-point correlation function of the operator (not equal to the identity) with smallest scaling dimension. More specifically, via a conformal map, the correction can be expressed in terms of the two-point function on a certain conical space with opening angle $2\pi n$. In the case of free conformal field theories, this two-point function can be computed explicitly using the method of images. We perform the computation for the conformally coupled scalar. From the $n \to 1$ limit of our results, we extract the leading thermal correction to the entanglement entropy, reproducing results of arXiv:1407.1358.